Let's analyze the functions in the image and match them to their respective graph descriptions.

1. $g(x) = -3x^2 + 3x$:

   • This is a quadratic function (it has an $x^2$ term), meaning its graph is a parabola.
   • The coefficient of $x^2$ is negative (-3), so the parabola opens downward.
   • Answer: Parabola opening down.

2. $f(x) = 5$:

   • This is a constant function, meaning no matter what $x$ is, $f(x)$ will always be 5.
   • The graph of a constant function is a horizontal line.
   • Answer: Horizontal line.

3. $h(x) = -3x - 3$:

   • This is a linear function in the form $y = mx + b$, where $m = -3$.
   • Since the slope is negative (-3), the graph is a line with a negative slope.
   • Answer: Line with a negative slope.

So, the correct answers are:

• (a) Parabola opening down
• (b) Horizontal line
• (c) Line with a negative slope

Would you like a detailed explanation of any of these functions?

Here are 5 related questions:

1. How do you determine the direction of a parabola from its equation?
2. What does the slope tell you about a line's orientation?
3. Can a quadratic equation ever represent a line?
4. Why is the graph of a constant function always a horizontal line?
5. How can you tell if a line has a positive or negative slope just by looking at its equation?

Tip: The sign of the leading coefficient in a quadratic equation determines whether the parabola opens up or down!